computational derivation of incident irradiance on ... · 1. that i am the sole author of the...

Computational Derivation of Incident Irradiance on Building Facades based on Measured Global Horizontal

Irradiance Data

A master's thesis submitted for the degree of“Master of Science”

Supervisor: Univ. Prof. Dipl. Ing. Dr. techn A. MahdaviDepartment of Building Physics and Building Ecology

Sokol Dervishi

Vienna, 27.06.2006

0426897

MSc Program "Building Science & Technology"

Affidavit

I, Sokol Dervishi hereby declare

1. That I am the sole author of the present Master Thesis, " Computational

Derivation of Incident Irradiance on Building Facades based on Measured

Global Horizontal Irradiance Data", 84 pages, bound, and that I have not used

any source or tool other than those referenced or any other illicit aid or tool, and

2. That I have not prior to this date submitted this Master Thesis as an examination

paper in any form in Austria or abroad.

Vienna, ___________________ _______________________________

Date Signature

2

ACKNOWLEDGEMENT

I would like to use the possibility to thank my supervisor Prof. Dr. Ardesir Mahdavi, the Head of the Department of Building Physics and Building Ecology, for guiding me towards the formulation and realization of in-depth research project. Prof. Mahdavi was a constant source of inspiration and motivation-always willing to critically review my results. His support, which was not only limited to my scientific work, made it very easy to have a very good time in his department.

I would like to express my special thanks to Miss Bojana Spasejovic, PhD candidate, who familiarized me with the area of my research thesis and highly helped me in achieving the results. Her limitless suggestions, critical comments, helpful hints and in particular, her vast helpfulness and motivational nature stimulated me and was very important during my work.

I would like to thank Mr. J. Lechleitner, Miss.L. Lambeva, PhD candidate and Mr. M. Mohammadi, PhD candidate, for their support toward the collection of data used in this paper and for their very friendly working atmosphere. Furthermore, I would like to specially thank Miss. L. Lambeva who helped me in understanding Solrad simulation program and providing computer support.

Finally, I would like to thank my parents, Hysen and Hysnie, and my two sisters Leonora and Silvana for making this effort worthwhile. This work is totally dedicated to them.

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Dedicated to my father, mother, Nora and Silvi

4

ABSTRACT

Reliable simulation of buildings' energy performance requires, amongst other things, the availability of detailed information on the magnitudes of incident solar radiation on building facades. However, the availability of the measured data concerning the incident solar radiation on vertical surfaces is restricted to only few locations. In addition, concurrent measurements of horizontal global and horizontal diffuse (or direct normal) irradiance data are likewise available only for a limited number of locations. In contrast, global horizontal irradiance data is available for many locations. This research demonstrates how to computationally derive incident irradiance values on vertical (or otherwise inclined) building surfaces from measured global irradiance values.

Given this context, three methods are considered to compute incident vertical irradiance values based on measured global horizontal irradiance data. Vertical solar irradiance measurements are described. Then, the computationally derived values are compared with corresponding measurements. The results are evaluated based on their correlation coefficients and relative error. Finally, the application of horizontal-to-vertical irradiance mapping is demonstrated using the case of an office building at Vienna University of Technology.

Keywords: horizontal and vertical irradiance, measurement and simulation, energy performance

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Table of Contents

1 INTRODUCTION 111.1 Motivation 111.2 Past research 12

2 APPROACH 143 MEASUREMENTS 15

3.1 Experiment overview 153.2 Measurements of horizontal illuminance 163.3 Data calibration 17

3.3.1 Uniform correction 183.3.2 Non-uniform correction 19

3.4 Average luminance of the sky sectors 193.5 Estimation of the vertical illuminance 213.6 Measurements of the vertical illuminance 243.7 Converting vertical illuminance to vertical irradiance 27

4 COMPUTATIONAL DERIVATION OF VERTICAL IRRADIANCES 294.1 H&K method 294.2 RAD method 334.3 “MET” method 36

5 RESUILTS 385.1 Comparison (H&K method) 385.2 Comparison (RAD method) 415.3 Comparison (MET method) 44

6 DISSCUSION 486.1 Comparison based on relative error 486.2 Variation in the methods’ performance over various sky conditions 52

7 CONCLUSION 607.1 Case Study 60

7.1.1 Overview 607.1.2 Approach 607.1.3 Results 63

7.2 Contribution 657.3 Potential for future work 66

REFERENCES 67Appendix A 69Appendix B 74Appendix C 79Appendix D 82

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List of Figures

Figure 1: Schematic diagram showing the necessary steps in order to estimate vertical

irradiance from horizontal illuminance ................................................................ 16

Figure 2: The sky monitoring device for measuring the illuminace due to the 12 sectors of

the sky hemisphere.............................................................................................. 17

Figure 3: Cumulative error describing the difference between the sum of 12 sensor values

and simultaneously measured global horizontal illuminance ................................ 17

Figure 4: Correction procedure for calibrating the measured data from the 12 sensors......... 18

Figure 5: 3D representation of the 12 sky sectors of the sky hemisphere showing the altitude

of the sky sector center and differential solid angle subtended by that sky sector for

the lower and upper sectors ................................................................................. 20

Figure 6: The representation of the angles of a certain patch that effect the vertical

illuminance ......................................................................................................... 22

Figure 7: Convention for calculating azimuth angle for north and east orientation .............. 23

Figure 8: Convention for calculating azimuth angle for south and east orientation .............. 23

Figure 9: Precise illuminance meters measuring the vertical illuminance for North, East

South and West façade ........................................................................................ 24

Figure 10: Comparison between the vertical illuminance values measured by illuminance

meters and the values derived from the sensors for the east façade....................... 25


meters and the values derived from the sensors for the South façade.................... 26


meters and the values derived from the sensors for the West façade..................... 26

Figure 13: The schematic procedure for deriving the vertical irradiance values using “H&K”

method. ............................................................................................................... 32

Figure 14: Schematic diagram of RAD method .................................................................. 35

Figure 15: Illustration for the procedure for deriving Vertical irradiance using “MET”

method................................................................................................................ 36

Figure 16: Diagram showing the interpolation procedure of the hourly vertical irradiance

values.................................................................................................................. 37

Figure 17 Comparison of measured and calculated (method: H&K) vertical irradiance values

(North façade) ..................................................................................................... 38


(East façade) ....................................................................................................... 39

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(South façade) ..................................................................................................... 39


(West façade) ...................................................................................................... 40


(All four orientations).......................................................................................... 40

Figure 22 Comparison of measured and calculated (method: RAD) vertical irradiance values

(North façade) ..................................................................................................... 41


(East façade) ....................................................................................................... 41

Figure 24 Comparison of measured and calculated (method: RAD vertical irradiance values

(South façade) ..................................................................................................... 42


(West façade) ...................................................................................................... 42


(all four orientations)........................................................................................... 43

Figure 27 Comparison of measured and calculated (method: MET) vertical irradiance values

(North façade) ..................................................................................................... 44


(East façade) ....................................................................................................... 44


(South façade) ..................................................................................................... 45


(West façade) ...................................................................................................... 45


(all four orientations)........................................................................................... 46

Figure 32 Comparison of cumulative error and percentage of results (method: H&K) of

vertical irradiance values (North, East; South and West façade) ........................... 48

Figure 33 Comparison of cumulative error and percentage of results (method: RAD) of


Figure 34 Comparison of cumulative error and percentage of results (method: MET) of


Figure 35 Comparison of cumulative error and percentage of results (methods: MET, RAD

and H&K) of vertical irradiance values (North façade) ........................................ 50


and H&K) of vertical irradiance values (East façade)........................................... 50

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and H&K) of vertical irradiance values (South façade) ........................................ 51


and H&K) of vertical irradiance values (West façade) ......................................... 51


and H&K) of vertical irradiance values, North, East, South and West). ................ 52


and H&K) of vertical irradiance values, North, East, South and West) under cloudy

sky conditions ..................................................................................................... 53


and H&K) of vertical irradiance values, North, East, South and West) under clear

sky conditions ..................................................................................................... 53

Figure 42 Comparison of the results under cloudy sky conditions (East)............................. 55

Figure 43 Comparison of the results under clear sky conditions (East)................................ 55

Figure 44 Comparison of the results under cloudy sky conditions (South) .......................... 56

Figure 45 Comparison of the results under clear sky conditions (South) ............................. 56

Figure 46 Comparison of the results under cloudy sky conditions (All orientations)............ 57

Figure 47 Comparison of the results under clear sky conditions (All orientations) .............. 57

Figure 48: Prediction vs measurement regression lines for the three methods (a: RAD, b:

H&K, c: MET).................................................................................................... 58

Figure 49 prediction vs measurement regression lines under cloudy sky conditions for the

three methods (a: RAD, b: H&K, c: MET) .......................................................... 58

Figure 50 prediction vs measurement regression lines under clear sky conditions for the

three methods (a: RAD, b: H&K, c: MET)......................................................... 59

Figure 51: The situation of the multi-storey educational building (Freihaus) and its

surrounding environment..................................................................................... 61

Figure 52: 3d model of the Freihause building................................................................... 62

Figure 53: Freihause building plan (5th floor) showing the offices directed to the East

orientation........................................................................................................... 62

Figure 54: Measured horizontal irradiance versus “RAD” and “H&K” methods (first week)63

Figure 55: Measured horizontal irradiance versus “RAD” and “H&K” methods (second

week) .................................................................................................................. 63

Figure 56: Measured horizontal irradiance versus “RAD” and “H&K” methods ................. 64

Figure 57: Measured horizontal irradiance versus “RAD” and “H&K” methods ................. 64


under cloudy sky conditions (North, East, South, West façade and All orientations)70

9





Figure 61: Comparison of cumulative error and percentage of results (method: H&K, RAD

and MET) of vertical irradiance values (North, East; South and West façade) ...... 72




and MET) of vertical irradiance values (All orientations)..................................... 73


under clear sky conditions (North, East, South, West façade and All orientations)75






and MET) of vertical irradiance values (North, East; South and West façade) ...... 77




and MET) of vertical irradiance values (All orientations)..................................... 78

Figure 70: The inputs of the H&K methods ........................................................................ 79

Figure 71: Defining the azimuth of each surface/point. ....................................................... 80

Figure 72: Obstacles’ angels for each point in three levels, close horizon, middle and far

horizon................................................................................................................ 80

Figure 73: A sample of the output file format (predefined in one hour basis) ..................... 81

Figure 74: The interpolation procedure using Sunselect software program......................... 81

Figure 75: Defining the inputs of the ‘MET’ to computationally derive vertical irradiance

values.................................................................................................................. 82

Figure 76: The parameters required (Global horizontal irradiance and outdoor temperature)

to computationally derive vertical irradiance values............................................. 83

Figure 77: The output format of MET ............................................................................... 83

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List of Tables

Table 1: Convention for calculating azimuth angle of the certain patch corresponding to the

certain orientation ............................................................................................... 24

Table 2: A sample of the input format of the model for defining the Vertical irradiance on

the façade............................................................................................................ 37

Table 3: Correlation between Measured and Predicted Values ............................................ 46

Table 4 Relative performance of the three methods with regards to the measured data ....... 54

Table 5: The parameters the case-study multi-storey educational building needed to define

the vertical irradiance values ............................................................................... 61

INTRODUCTION

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1 INTRODUCTION

1.1 Motivation

Availability of reliable information on the magnitudes of incident solar radiation on building facades is required for a number of applications concerning the effective utilization of solar energy. For example, such information is important in view of

• Dependable simulation on the energy performance of building in general and solar gains in particular

Building Energy simulation programs have the potential to optimize the perimeter zone energy balance between daylight admission and solar heat gain rejection (Lee et al. 2000). They are valuable design and analysis tools to evaluate the solar radiation levels by assessing the energy performance of building envelope savings and cooling energy requirements (Danny et al. 1999). However, detailed information on the magnitudes of incident solar radiation on building facades is required for the reliability of building simulation on buildings energy performance to maintain the balance between cooling/heating and lighting energy (Vine et al. 1998) associated with solar heat gains and to support decisions regarding the selection and integration of energy saving building components (Cornelis and De Wilde 1998).

• Design of exterior and interior shading devices

Shading devices are often used in buildings mainly to reduce cooling energy use, but also to control glare and day-lighting (Bülow 2000). Most occupants avoid the presence of sun light by activating the shading devices in order to block the direct sunlight. Solar radiation reaches the windows directly from the sun or indirectly from the sky and surroundings. A part of it is absorbed or reflected and the remaining part is transmitted to the indoor spaces (Dijk 1987). There is a need for a detailed knowledge of the solar radiation on vertical surfaces to optimize the use and design of advanced exterior and interior shading devices, and thus efficiently control the solar gains and day-lighting through windows.

INTRODUCTION

12

• Effective real-time control of shading devices without the need for intricate measurement devices

A major cause of high energy use and occupant discomfort is the large variation in daylight availability and solar radiation due to seasonal changes in sun position and cloud cover (Vine et al 1998). Automated shading devices are operated to block the direct sun and permit view in response to changing solar conditions and occupant-set preferences. They are automatically lowered as soon as incoming solar irradiance hits the workplace (Selkowitz and Lee 1998). For this purpose the vertical irradiance values play an important role.

A crucial input required in the simulation of solar energy systems is the radiation incident on facades. However, only for relatively few locations detailed measured data concerning incident solar radiation on vertical (or otherwise inclined) surfaces are available. Concurrent measurements of horizontal global and horizontal diffuse (or direct normal) irradiance data are likewise available only for a limited number of locations. In contrast, the measurement of global horizontal irradiance is rather simple and cost-effective. It can be, conceivably, an integral part of the sensory equipment of every building. The question is, then, if incident irradiance values on vertical (or otherwise inclined) building surfaces can be computationally derived from measured global irradiance levels in a manner both reliable and convenient.Given this context, three methods to compute incident vertical irradiance values based on measured global horizontal irradiance values are applied. Then computationally derived values with corresponding measurements to rank the methods' performance are compared.

1.2 Past research

To computationally derive vertical irradiance data from measured irradiance levels reliable information on the magnitudes of incident solar radiation on building facades is necessary to determine the fraction which is diffuse (or direct) then estimating the diffuse and direct component on an inclined surface of every orientation.

Most models are similar when modeling the direct and reflected components, but the main difference arises when modeling the diffuse components. There have been some efforts in estimating direct and diffuse components (vertical irradiance values) from the measured global horizontal irradiance values as input to computationally derive vertical irradiance value on an inclined surface. Early work by Liu and Jordan (Liu and Jordan 1960) show a relationship between the daily diffuse and daily total

INTRODUCTION

13

radiation on a horizontal surface defining an interrelationship and characteristic distribution of diffuse and total solar radiation. The diffuse fraction is defined as a function of the hourly clearness index (ratio of hourly global horizontal to hourly extraterrestrial radiation). Orgill and Hollands (Orgill and Hollands 1977) and Erbs et al (Erbs at al. 1980) developed correlation equations for hourly diffuse radiation on a horizontal surface. Build on their work, Duffie and Beckam (Duffie and Beckam 1980) used an index, ck , where “clear sky” radiation, cI replaces extraterrestrial in the definition of ck . Based on this research, Garrison 1995 developed the correlation

of diffuse and direct components by illustrating the dependence of diffuse fraction on surface, atmospheric precipitable moisture, atmospheric turbidity, solar elevation and global horizontal radiation.

Perez and Seals (Perez and Seals 1990) compute the irradiance components on a titled surface based on direct and total global irradiance. They define equations to vertically derive the measured horizontal irradiance values using the direct and diffuse components. In addition, they create a new simplified version of the diffuse radiance model for titled surfaces. Based on their model, Robledo and Solaer (Robledo and Solaer 1996) developed some coefficients to computationally derive the vertical irradiance values based on direct and diffuse components.

However, less research has been made in evaluating the computationally derived vertical irradiance values amongst different methods. This research is focused on comparing three methods defined here as H&K, RAD, and MET to compute vertical irradiance values based on measured global horizontal irradiance values.

APPROACH

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2 APPROACH

Three methods were considered to computationally derive vertical irradiance values from measured global horizontal irradiance values. The first method is a procedure that is suggested by Heindl and Koch 1976 (referred here as “H&K”). Based on time, location, orientation of the surfaces as well as a number of meteorological parameters, the incident solar radiation on arbitrary surfaces is calculated. The second method (referred here as “RAD”) involves the simulation application RADIANCE (Ward Larson and Shakespeare 2003). Perez All- weather sky model (Perez at al. 1993) is the sky model which is used to simulate the incident radiation on vertical surfaces. Direct normal and diffuse horizontal radiations are the input requirements for the model. The algorithm suggested by Reindl (Reindl et al. 1990)is used. The algorithm allows deriving the diffuse components from corresponding measured global horizontal irradiance values. The direct normal values are derived from the direct horizontal irradiance values. The third method (referred here as “MET” involved the use of the METEONORM simulation application (Meteonorm 2005). The radiation incident on arbitrary incident surfaces is estimated based on the available horizontal irradiance and outdoor temperature values.

Over a period of 16 days, the illuminance levels at 12 sensors inside a montoring device and global horizontal irradiance as well as vertical illuminance levels on 4 vertical facades (North, East, South and West) were measured in a 15 minute interval. From measured illuminance levels, corresponding irradiance levels were derived using luminous efficacy. The calculated and predicted results are compared. The application of horizontal-to-vertical irradiance mapping was demonstrated using the case of an office building in Vienna University of Technology. The case study investigates the implications of “RAD” and “H&K” for the computational prediction of the vertical irradiance values for east façade. The building situation and the surrounding environment are taken into the consideration.

MEASUREMENTS

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3 MEASUREMENTS

Monitoring of the outdoor solar radiation in this experiment has been obtained indirectly, using the corresponding photometric measurements.

Outdoor solar radiation monitoring was performed during one week in November 2005 and one week in April 2006. During the measurements in November 2005, only the measurements of horizontal illuminance were available. Thus, the vertical illuminance estimations were derived based on the measurements of horizontal illuminance due to corresponding portions of the sky hemisphere. Measurements obtained in April 2006 included the measurements of vertical illuminance in North, East, South and West direction. Using the luminous efficacy, defined as the ratio of simultaneously measured global horizontal illuminance and irradiance, the vertical illuminance values were further converted into vertical irradiance.

3.1 Experiment overview

A sky monitoring device, designed at the Department of Building Physics and Building Ecology of Vienna University of Technology (Spasojevic and Mahdavi 2005) has been used to monitor the horizontal illuminance due to 12 equally-sized sky hemisphere sectors. This device was placed on the roof of a university building. Simultaneously, the global horizontal illuminance has been measured by a precision illuminance meter and the measurements of the global irradiance have been obtained from the nearby weather station.

The data gathered from the sensors are stored by using the “Data-Log-Datasocket” software program and calibrated based on the measured global horizontal illuminance values. Based on calculated average luminance of the 12 sky sectors, the corresponding vertical illuminance on the North, East, South and West façade have been estimated. Luminous efficacy, calculated as a ratio of measured global illuminance and simultaneously measured global irradiance has been used to convert the calculated vertical illuminance into vertical irradiance on the North, East, South and West facades. The schematic explanation of this procedure is shown in figure 1.

MEASUREMENTS

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Figure 1: Schematic diagram showing the necessary steps in order to estimate vertical irradiance from horizontal illuminance

3.2 Measurements of horizontal illuminance

A sky monitoring device was used to monitor the outdoor conditions in terms of horizontal illuminance due to different sectors of the sky. This monitoring device consists of 12 cells organized in three levels. One illuminance sensor is placed in each cell. Due to the arrangement of the cells and positions of the quadratic apertures, every sensor receives light from one of the 12 equally sized sky sectors Each sky sector comprises a solid angle of π /6 steradians (Spasojevic and Mahdavi 2005). Figure 4 illustrates the sky monitoring device.

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Figure 2: The sky monitoring device for measuring the illuminace due to the 12 sectors of the sky hemisphere

3.3 Data calibration

To empirically evaluate the sensor’s performance, the sum of the illuminance levels, measured by 12 sensors, were compared with the simultaneously measured global horizontal illuminance. The sum of the horizontal illuminance measured by sensors theoretically should be equal to the global horizontal illuminance measured by the precise illuminance meter. However, the results show that there is a difference between the sum of the values measured by sensors and the measured global horizontal illuminance. The figure 2 explains the relative error.

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50Cumulative Error [+- %]

Per

cent

age

of R

esui

lts [

%]

Figure 3: Cumulative error describing the difference between the sum of 12 sensor values and simultaneously measured global horizontal illuminance

As figure 2 implies, some of the 38% of the data show a relative error les than 5%. More than 90% of the data measured has a relative error less than 25% and all the

MEASUREMENTS

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data has a relative error less than 40 %. Based on the comparison, the sensor-based data need to be calibrated. The illuminance sensors used in this experiment can reliably measure up to 20000 lx. Thus, in cases when none of the sensors within the monitoring device measures more than 20000 lx, the uniform correction can be applied. In cases when one of the sensors exceeds 20000 lx, a non-uniform correction is needed. Figure 3 illustrates the correction procedure.

Figure 4: Correction procedure for calibrating the measured data from the 12 sensors.

3.3.1 Uniform correction

The uniform correction factor is calculated as a ratio of measured global illuminance and the sum of horizontal illuminance values measured by twelve sensors within the sky monitoring device.

∑=

=12

iiglobaluniform EECF (1)

Where:

globalE measured global horizontal illuminance

unformCF uniform correction factor

iE horizontal illuminance measured by a single sensor

The horizontal illuminance values, measured by each of the twelve sensors, are then multiplied with the uniform correction factor:

MEASUREMENTS

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iuniformcorrectedi ECFE ⋅=)( (2)

This correction makes it possible to account for the imprecision of the sensors (specified tolerance is ± 10%) when they are exposed to the illuminance levels.

3.3.2 Non-uniform correction

At the beginning, the average uniform correction factor is defined. This factor is calculated as the average value of the uniform correction factors for the cases when the uniform correction can be applied.

The horizontal illuminance values, measured by each of the twelve sensors are then multiplied with the average uniform correction factor:

iavguniformcorrectedi ECFE ⋅= )()( (3)

In the next step, the difference between the global horizontal illuminance and the sum of the 12 corrected sensor values is calculated as:

∑=

−=∆12

1)(

icorrectediglobal EE (4)

Where:

∆ difference between the global horizontal illuminance and the sum of the 12 corrected sensors values

This difference is finally added to the highest corrected sensor value (exceeding 20000 lx):

∆+= max)max( EE corrected (5)

3.4 Average luminance of the sky sectors

As already explained, a sky monitoring device was used to monitor the outdoor conditions in terms of horizontal illuminance due to different sectors of the sky. Each of 12 sensors inside the monitoring device receives light from one sky sector comprising π /6 sr solid angle. These 12 sectors of the sky hemisphere are shown in figure 5.

MEASUREMENTS

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Figure 5: 3D representation of the 12 sky sectors of the sky hemisphere showing the altitude of the sky sector center and differential solid angle subtended by that sky sector for the lower and

upper sectors

The contribution of a certain patch of the sky hemisphere to the horizontal illuminance on a point in the center of the hemisphere is determined by luminance of the patch, the solid angle subtended by that patch and its altitude (Spasojevic and Mahdavi 2005):

iiii LE ∆Ω⋅⋅= θsin (6)

where

iE illuminance on a horizontal plane due to a particular sky patch

iL luminance of a sky patch

iθ altitude of the sky patch center

∆ Ω i differential solid angle subtended by the sky patch

Consequently, if the illuminance on a horizontal plane, due to a particular sky sector is known, the average luminance of that sky sector can be calculated as follows:

ii

ii

EL∆Ω⋅

=θsin

(7)

MEASUREMENTS

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In this case, as shown in figure 5, the sky hemisphere is composed of 12 sky sectors organized in two levels. Their solid angles are known (π /6 sr), the resulting illuminance level are monitored by the illuminance sensors inside the sky monitoring device. The altitudes of the sector centers are extracted from the respective three dimensional solids as:

°= 46.20iθ for the lower sectors of sky hemisphere which correspond to the first

and the second layer of the monitoring device and

°= 36.60iθ for the upper sectors of sky hemisphere which correspond to the

third layer of the monitoring device

3.5 Estimation of the vertical illuminance

To increase the precision of integration while calculating the vertical illuminance on the North, East, South and West façade, the sky dome is subdivided in 256 smaller patches (Spasojevic and Mahdavi 2005). According to its position on the sky hemisphere, each of these 256 patches is assigned the average luminance of the corresponding sky sector, detected in the same portion of the sky. The calculation of the average luminance of the 12 sky sectors of the sky hemisphere is described in the previous section.

The contribution of a sky patch with known luminance and solid angle to the illuminance on a vertical surface depends on its altitude (θ i) and ”azimuth” angle to the particular vertical surface (ϕ i). The “azimuth” angle between patch and a

particular vertical plane is defined as the angle between the horizontal projection of the line connecting the center of the hemisphere with the center of the patch and that vertical plane. An example of a sky patch (according to the proposed 256-patch pattern) and its relation to one (in this example, west oriented) vertical plane is shown in figure 6.

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Figure 6: The representation of the angles of a certain patch that effect the vertical illuminance

The resulting illuminance on the vertical plane is defined per equation 8:

iiiiiv LE ϕθ sincos ⋅⋅∆Ω⋅= (8)

If the angular dimensions ( ∆ ϕ and ∆ θ ) are known, the vertical illuminance is

defined as follows:

iiiiiv LE ϕθθϕθ sincoscos ⋅⋅⋅∆⋅∆⋅= (9)

Where

Eiv illuminance on a vertical plane due to a particular sky patch

iL luminance of a sky patch

ϕ∆ angular size of a patch in azimuth direction

∆ θ angular size of a patch in altitudinal direction

iθ altitude of the sky patch center

iα ”azimuth” angle between surface and horizontal projection of the line

which connects center of the sky patch and measurement point

The azimuth and altitude of the sky patch center corresponding to the certain orientation is defined per figure 7 and 8.

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Figure 7: Convention for calculating azimuth angle for north and east orientation

Figure 8: Convention for calculating azimuth angle for south and east orientation

As figures 7 and 8 imply, the same patch contributes to horizontal illuminance of two orientations. The patch in the figure 7 contributes to both north and the south orientation. The table 1 explains the conventions for calculating the azimuth angle of the certain patch which corresponds to the certain orientation. The azimuth angle for the north orientation starts from West, while for the east orientation starts from the North. The azimuth angle for the South orientation starts from East, while for the west orientation starts from South.

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Table 1: Convention for calculating azimuth angle of the certain patch corresponding to the certain orientation

Orientation Starting from

North Clock-wise starting from West

East Clock-wise starting from North

South Clock-wise starting from East

West Clock-wise starting from South

A half of the sky hemisphere contributes to the vertical illuminance on a certain façade. According to this rule, for each orientation a corresponding half of the hemisphere is detected and considered within the calculation procedure. Using the convention described in figures 7-8 and table 1, the respective azimuth angles of the sky patches are defined for each orientation. Finally, the contributions of the sky patches to the vertical illuminance for particular orientations are calculated as per equation 9.

3.6 Measurements of the vertical illuminance

Besides the measurements of horizontal illuminance using monitoring device and the measurements of the global horizontal illuminance and irradiance, the simultaneous measurements of vertical irradiances were additionally performed during a week in April 2006. Global horizontal illuminance and irradiance were obtained from the nearby weather station. Figure 9 illustrates the arrangement of the precision illuminance meters attached to the sky monitoring device for the measurements of the vertical illuminance.

Figure 9: Precise illuminance meters measuring the vertical illuminance for North, East South and West façade

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In order to prevent the reflected light beams, the illuminance meters were protected by black caps, as illustrated in figure 9.

The measured values for vertical illuminance on the east, south and west façade were compared to the values derived from the 12 sensors within the sky monitoring device. Most of the data derived from the sensors lie in the range below 45000 lx. The values which are above 45000 lx are not very reliable because of the limitations of the sensory equipment. The figures 10-12 show the resulting correlations between the vertical illuminance values for these three orientations (east, south and west), measured by illuminance meters and the ones derived from the horizontal illuminance values obtained from the sensors within the sky monitoring device. Figure 10 shows the correlation between the values measured by illuminance meters and the values derived from the sensors for the East façade, aiming at 0.91.

y = 0,9475x+ 1472R2 = 0,9117

05000

1000015000200002500030000350004000045000

0 10000 20000 30000 40000 50000

values measured from illuminance meter [lux]

valu

es m

easu

red

from

12

sens

ors [

lux]

Figure 10: Comparison between the vertical illuminance values measured by illuminance meters and the values derived from the sensors for the east façade

The correlation of the vertical illuminance on the south façade is higher than on the east façade, aiming at 0.93 (Figure 11).

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y = 0,9292x + 1380,9R2 = 0,9322

05000

100001500020000250003000035000400004500050000

0 10000 20000 30000 40000 50000


valu

es m

easu

red

from

12

sens

ors [

lux]

Figure 11: Comparison between the vertical illuminance values measured by illuminance meters and the values derived from the sensors for the South façade

The correlation between measured and derived values of the vertical illuminance on the west façade is lower than for east and south orientations. Still the correlation aims at 0.85 in this case (see Figure 12).

y = 1,0454x + 997,41R2 = 0,8531

05000

100001500020000

2500030000350004000045000

0 10000 20000 30000 40000 50000


valu

es m

easu

red

from

12

sens

ors [

lux]

Figure 12: Comparison between the vertical illuminance values measured by illuminance meters and the values derived from the sensors for the West façade

MEASUREMENTS

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Based on considerably high correlations between measured and derived values for the vertical illuminance on the east, south and west façade, shown in figures 10-12, it can be concluded that the values derived from the measurements of the horizontal illuminance according to the previously described procedure can reliably represent the expected vertical illuminance on these façades. It can be expected that the vertical illuminance on the north façade can be reliable derived from the measurements of horizontal illuminance and the estimated average (uniform) luminance of the respective sky sectors. Thus, the final data set, which will be considered in the further analysis, consists of: a) measured vertical illuminance on the east, south and west façade for one week in April 2006; b) derived vertical illuminances on the north, east, south and west façades for a week in November 2005 and for the north façade for one week in April 2006, based on the measurements of horizontal illuminance using sky monitoring device.

3.7 Converting vertical illuminance to vertical irradiance

Vertical illuminance values for the north, east, south and west facades can be converted to vertical irradiance values using luminous efficacy. As the simultaneous measurements of the global illuminance and irradiance were available during aforementioned two weeks of measurements, the respective luminous efficacy values can be calculated as a ratio of measured global horizontal illuminance to measured global horizontal irradiance:

=

==

Wlm

mWmlm

GE

h

h2

2

η (10)

where

η Luminous efficacy

Eh Global horizontal illuminace

Gh Global horizontal irradiance

MEASUREMENTS

28

Consequently, after having either estimated or measured the vertical illuminances on the north, east, south and west façades during one week in November 2005 and one week in April 2006, the calculated luminous efficacy values are used to estimate the respective vertical irradiances:

ηV

vEG = (11)

where

Ev Vertical illuminance incident on a facade

Gv Vertical irradiance incident on a façade

COMPUTATIONAL DERIVATION OF VERTICAL IRRADIANCES

29

4 COMPUTATIONAL DERIVATION OF VERTICAL IRRADIANCES

As already mentioned, three methods were considered to computationally derive vertical irradiance values from measured global horizontal irradiance: H&K, RAD and MET.

4.1 H&K method

The first method (referred here as H&K) used to computationally derive vertical solar irradiance values from measured global horizontal irradiance data is based on a procedure suggested by Hendl and Koch (Hendl and Koch 1976). This method calculates the diffuse and direct horizontal irradiance data as well as diffuse and direct vertical irradiance levels in any inclined surfaces. The inputs needed to compute the values are:

§ Geographic coordinates

§ See level

§ The azimuth of each surface needs to be defined.

§ Obstacles

§ Turbidity factor

The user specifies the metrological data at a particular location. The output produces global horizontal irradiance (with the direct and diffuse components) as well as the vertical irradiance (with the direct and diffuse components) for North, East, South and West in hourly basis. The data is delivered in a predefined format. The next step is the interpolation (15 minute basis) procedure using Sunselect software program (see Appendix C).

An algorithm is needed to perform the vertical irradiance values based on the measured global horizontal irradiance data.

E (Derived Vertical) = E (H&K-Vertical Diffuse.) + E (H&K-Vertical Direct) * D (12)


30

D = [E (“Measured” Horiz. Direct) /E (Solrad Horiz. Direct)] (13)

As the equation 12 implies, the vertical irradiance values derived for North, East, South and West is the sum of the vertical diffuse and direct components. However, the direct component is multiplied with a factor which is the ratio of measured global irradiance values to the direct component of the horizontal irradiance computed by H&K (equation 13).

If the measured global horizontal irradiance values are lower than the computed diffuse horizontal irradiance an equation representing uniform cloudy situations is applied. To calculate the vertical irradiance on the façades, the diffuse vertical component is multiplied with a factor which is the ratio of measured global horizontal irradiance values (measured by the weather data station) to the diffuse horizontal irradiance. Equation 14 explains the procedure.

If ≤)(hiG diffusehiG )(

−

diffusevi

diffusehi

hivi G

G

GG )(

)(

)()( ⋅= − (14)

Where:

)(viG derived vertical irradiance

hiG )( global horizontal irradiance

Gi v direct( ) direct vertical component

Gi v diffuse( ) diffuse vertical component

directhiG )(

−

direct horizontal irradiance

diffusehiG )(

−

diffuse horizontal irradiance

However, if the measured global horizontal irradiance values are higher than the computed diffuse horizontal irradiance, the non uniform clear sky condition equation is applied. In this case, the direct vertical component is multiplied with another factor which is the ratio of the difference between measured horizontal irradiance and computed diffuse horizontal irradiance to the computed direct horizontal irradiance.


31

These values are added to the diffuse vertical component. The equation 15 explains the procedure.

If G Gi h i h diffuse( ) ( )≥

GG G

GG Gi v

i h i h diffuse

i h directi v direct i v diffuse( )

( ) ( )

( )( ) ( )=

−⋅

+ (15)

Where:

)(viG derived vertical irradiance

hiG )( global horizontal irradiance

Gi v direct( ) direct vertical component

Gi v diffuse( ) diffuse vertical component

directhiG )(

−

direct horizontal irradiance

diffusehiG )(

−

diffuse horizontal irradiance


32

The figure below explains the overall conversion of the vertical irradiance values based on “H&K” methods.

Figure 13: The schematic procedure for deriving the vertical irradiance values using “H&K” method.


33

4.2 RAD method

This method involves the use of RADIANCE lighting simulation system (Ward Larson and Shakespeare 2003). Perez All-weather sky (Perez et al. 1993) was used as the underlying sky model.

Perez All-weather sky model requires the input of both diffuse horizontal and direct normal irradiance. As the measurements for these parameters were not available during this experiment, the diffuse horizontal component is derived from the measured global horizontal irradiance. In order to derive the diffuse fractions from the measured global horizontal irradiance, the algorithm suggested by Reindl et al. was used (Reindl et al. 1990). This algorithm considers following parameters: clearness index (kt), sun altitude (a) (Solar altitude 2005), outdoor air temperature (Ta) and the relative humidity (φ). The measurements of global horizontal irradiance, outdoor air temperature and the relative humidity were obtained from the weather station of the Department of Building Physics and Building Ecology of Vienna University of Technology.

Reindl et al. identified three characteristic intervals for clearness index, defined as the ratio of global horizontal to extraterrestrial radiation. Depending on clearness index value, the diffuse fractions (Id/I) are calculated as per equations 16-18 (Reindl et al. 1990):

i) 3.00 ≤≤ tk Constraint: 0.1/ ≤IId

( ) φα 0195.0000682.0sin0239.0232.000.1/ +−+−= atd TkII (16)

ii) 78.03.0 ≤≤ tk Constraint: 1.0/ ≥II d & 97.0/ ≤II d

( ) φα 106.000357.0sin267.0716.1329.1/ +−+−= atd TkII (17)

iii) tk≤78.0 Constraint: 1.0/ ≥II d

( ) φα 0734.000349.0sin256.0426.0/ +−−= atd TkII (18)


34

where

I global horizontal irradiance

Id diffuse horizontal irradiance

kt clearness index

a sun altitude

Ta outdoor air temperature

φ relative humidity

After having calculated diffuse fractions, diffuse horizontal irradiance and normal direct irradiance, are calculated as follows:

IIk ddiff /= (19)

diffd kII ⋅= (20)

dbh III −= (21)

)sin(/ αbhbn II = (22)

where

kdiff global horizontal irradiance

Ibh direct horizontal irradiance

Ibn direct normal (beam) irradiance

Ta outdoor air temperature


35

Diffuse horizontal irradiance and direct normal irradiance provide the input data for Perez All-weather model for sky luminance distribution, used as the underlying sky model for simulations performed with RADIANCE lighting simulation system. The overall schematic diagram of RAD method is given in figure 14.

Figure 14: Schematic diagram of RAD method


36

4.3 “MET” method

The third method (referred here to as "MET") involved the use of the application METEONORM (Meteonorm 2005). This application allows for the estimation of radiation incident on arbitrarily oriented surfaces based on available measured global horizontal irradiance and outdoor air temperature values. The method, based on algorithms and database according to a scheme that is predetermined, precedes the radiation resolution into diffuse and direct components. Then the program calculates the vertical irradiance values with a defined inclination and azimuth (Appendix D). Figure 15 illustrates the procedure.

Input Output

Figure 15: Illustration for the procedure for deriving Vertical irradiance using “MET” method

The user specifies the metrological data at a particular location. The measurements of global horizontal irradiance and outdoor air temperature, as inputs to computationally derive the vertical irradiance values on any inclined surfaces, were obtained from the weather station of the Department of Building Physics and Building Ecology of Vienna University of Technology. The data is then interpolated with hourly average (defined input) and then arranged in a required format. Table 2 illustrates a sample of the input format


37

Table 2: A sample of the input format of the model for defining the Vertical irradiance on the façade

Month Day of the month Day of the year Horiz. irradiance Outdoor temperature

1 1 1 373 6

1 1 2 534 2

1 1 3 695 -3

1 1 4 856 3

1 1 5 1017 4

1 1 6 212 -3

1 1 7 373 -4

1 1 8 572 -6

1 1 9 787 -5

For comparison purposes, output data of the vertical irradiance values is interpolated in 15 minutes step. The ratio of vertical irradiance in hourly basis derived by “MET” to the horizontal global irradiance obtained from the weather station is compared to the ratio of vertical irradiance to the horizontal global irradiance in 15 minute step. Using this equation, the Vertical Irradiance for 15 minute step is defined. The equation 23 and the figure 16 illustrate the relationship.

min)15(

min)15(

)(

)(

h

v

hourlyh

hourlyv

GG

GG

= (23)

Figure 16: Diagram showing the interpolation procedure of the hourly vertical irradiance values

RESUILTS

38

5 RESUILTS

Computationally derived vertical irradiances values of H&K, RAD and MET methods are compared with measured vertical irradiance values based on their correlation and relative error. A total of about 300 pairs of measured-predicted vertical irradiance values were used to determine the correlation ( r 2 ) and the relative error between the measurements and predicted derived of each model for North, East, South, West and All-Orientation.

5.1 Comparison (H&K method)

Figures 17-20 illustrate the relationship between the computationally derived vertical irradiance values based on ‘H&K’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for North, East, South and West direction. Their correlation coefficient of their linear regression is defined.

y = 0.8446x - 8.4603R2 = 0.6163

020406080

100120140160180200

0 20 40 60 80 100 120 140 160Computed values using "H&K" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 17 Comparison of measured and calculated (method: H&K) vertical irradiance values (North façade)

RESUILTS

39

y = 0.9492x - 13.836R2 = 0.8063

0

100

200

300

400

500

600

0 100 200 300 400 500 600Computed values using "H&K" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 18 Comparison of measured and calculated (method: H&K) vertical irradiance values (East façade)

y = 1.005x - 73.943R2 = 0.8951

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "H&K" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m •

² ]

Figure 19 Comparison of measured and calculated (method: H&K) vertical irradiance values (South façade)

RESUILTS

40

y = 0.7731x - 11.103R2 = 0.8305

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800Computed values using "H&K" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 20 Comparison of measured and calculated (method: H&K) vertical irradiance values (West façade)

Figure 21 illustrates the relationship between the computationally derived vertical irradiance values based on ‘H&K’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for all orientations. The correlation coefficient of this linear regression is 0.88.

y = 0.8768x - 20.491R2 = 0.8762

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "H&K" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 21 Comparison of measured and calculated (method: H&K) vertical irradiance values (All four orientations)

RESUILTS

41

5.2 Comparison (RAD method)

Figures 22-25 illustrate the relationship between the computationally derived vertical irradiance values based on ‘RAD’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for North, East, South and West direction. Their correlation coefficient of their linear regression is defined.

y = 1.4232x - 11.67R2 = 0.8337

020406080

100120140160180200

0 20 40 60 80 100 120 140Computed values using "RAD" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 22 Comparison of measured and calculated (method: RAD) vertical irradiance values (North façade)

y = 0.8383x + 13.989R2 = 0.8741

0

100

200

300

400

500

600

0 100 200 300 400 500 600Computed values using "RAD" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m •

² ]

Figure 23 Comparison of measured and calculated (method: RAD) vertical irradiance values (East façade)

RESUILTS

42

y = 1.0031x - 31.097R2 = 0.9374

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "RAD" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 24 Comparison of measured and calculated (method: RAD vertical irradiance values (South façade)

y = 0.7697x + 26.479R2 = 0.7627

0

100

200

300

400

500

600

700

0 200 400 600 800Compued values using "RAD" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 25 Comparison of measured and calculated (method: RAD) vertical irradiance values (West façade)

RESUILTS

43

Figure 26 illustrates the relationship between the computationally derived vertical irradiance values based on ‘RAD’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for all orientations.The correlation coefficient of this linear regression is 0.90.

y = 0.8969x + 7.9209R2 = 0.902

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "RAD" [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•² ]

Figure 26 Comparison of measured and calculated (method: RAD) vertical irradiance values (all four orientations)

RESUILTS

44

5.3 Comparison (MET method)

Figures 27-30 illustrate the relationship between the computationally derived vertical irradiance values based on ‘MET’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for North, East, South and West direction. Their correlation coefficient of their linear regression is defined.

y = 0,4164x + 20,422R2 = 0,5738

020406080

100120140160180

0 100 200 300 400Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[ W

• m

•² ]

Figure 27 Comparison of measured and calculated (method: MET) vertical irradiance values (North façade)

y = 0,5538x + 7,4927R2 = 0,82

0

100

200

300

400

500

600

0 200 400 600 800 1000Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[ W

• m

•² ]

Figure 28 Comparison of measured and calculated (method: MET) vertical irradiance values (East façade)

RESUILTS

45

y = 0,8143x - 3,9399R2 = 0,8896

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "MET" [ W• m •² ]

Mea

sure

d va

lues

[ W

• m

•² ]

Figure 29 Comparison of measured and calculated (method: MET) vertical irradiance values (South façade)

y = 0,8219x + 3,3791R2 = 0,7953

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[ W

• m

•² ]

Figure 30 Comparison of measured and calculated (method: MET) vertical irradiance values (West façade)

RESUILTS

46

Figure 31 illustrates the relationship between the computationally derived vertical irradiance values based on ‘RAD’ method (horizontal axis) and the measured vertical irradiance values (vertical axis) for all orientations.The correlation coefficient of this linear regression is 0.90.

y = 0,776x - 7,5321R2 = 0,853

0100200300400500600700800900

0 200 400 600 800 1000Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[ W

• m

•² ]

Figure 31 Comparison of measured and calculated (method: MET) vertical irradiance values (all four orientations)

The resulting correlation coefficients (r2) for all the methods (North, East, South and West orientations) are summarized in table 3.

Table 3: Correlation between Measured and Predicted Values

Correlation (r 2) [-]Model North Orient. East Orient. South Orient. West Orient. All Orient.H&K 0.61 0.81 0.9 0.83 0.88RAD 0.83 0.87 0.94 0.76 0.90MET 0.57 0.82 0.89 0.79 0.85

H&K method appears to give good results in terms of correlation. The correlation coefficient of the linear regression between the simulated irradiance values and the measured ones for all orientations is 0.88 (figure 21). The North façade has a quite low correlation (0. 61) in comparison to the other orientations but still the values till 100 2−⋅mW are near to the regression line. The south façade shows the highest correlation (0, 90) (figure 19). Computationally derived vertical irradiance values mainly overestimate. The north façade has the highest overestimation (figure 17).

RESUILTS

47

The results in the section above show that RAD has the highest correlation in comparison to the other methods. The correlation coefficient of the linear regression between the simulated irradiance values and the measured ones for all orientations is 0.90 (figure 26). The west façade has the lowest correlation (0.76) and the South facade has the highest one (0.90) in comparison to the otherorientations. The computed values mainly overestimate. However, the irradiance values show an underestimation (figure 24) when the model faces to the south.

MET method appears to have the low correlation. As H&K method, The North façade has the lowest correlation (0. 57) in and the south façade has the highest correlation (0, 89) in comparison to all orientations (figure 31). The computed values in every orientation overestimate.

DISSCUSION

48

6 DISSCUSION

6.1 Comparison based on relative error

To obtain the intuitive sense of the deviations between measured and predicted values, the relative error (RE) was calculated for each reference point according to the following equation:

REcalculated measured

measured=

−⋅ 100 [%] (24)

Based on the criteria of a small range of error, the relative error versus the percentage of results is defined for all methods (H&K, RAD and MET). Then, the methods are compared and the best performance amongst them considered in the research is defined. Figures 32-34 illustrate the percentage of the values according to the relative error of North, East, South and West orientations for each model. Figure 32 corresponds to H&K method; Figure 33 to RAD method andfigure 34 to MET method.

0

1020304050

60708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ]

Per

cent

age

of R

esul

ts [

% ]

North East South West

Figure 32 Comparison of cumulative error and percentage of results (method: H&K) of vertical

irradiance values (North, East; South and West façade)

DISSCUSION

49

010

203040

5060

7080

90100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]


Figure 33 Comparison of cumulative error and percentage of results (method: RAD) of vertical irradiance values (North, East; South and West façade)

0

10

20

30

40

5060

7080

90100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]


Figure 34 Comparison of cumulative error and percentage of results (method: MET) of vertical


Based on their relative error, H&K, RAD and MET are compared for each orientation separately. The aim is to explore the performance according to each orientation differs amongst the methods. The figures 35- 38 illustrate the resultsof the methods for North, East, South and West façade respectively.

DISSCUSION

50

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"

Figure 35 Comparison of cumulative error and percentage of results (methods: MET, RAD and

H&K) of vertical irradiance values (North façade)

01020304050

60708090

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"


H&K) of vertical irradiance values (East façade)

DISSCUSION

51

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RED" "H&K"


H&K) of vertical irradiance values (South façade)

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"


H&K) of vertical irradiance values (West façade)

DISSCUSION

52

Figure 39 illustrates the relative error comparison of H&K, RAD and MET for all orientations.

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"


H&K) of vertical irradiance values, North, East, South and West)

As Figure 39 illustrates, RAD (computation using RADIANCE and the Reindl algorithm) shows the lowest relative error amongst the three methods considered in this research while MET and H&K imply high relative errors. Some 55% of RAD data (measurement-calculation comparisons for all four directions) show a relative error less than 20%. Some 85% of data show a relative error of less than 50%. However, more that 55% of data for MET and H&K show a relative error more than 50%.

6.2 Variation in the methods’ performance over various sky conditions

Based on the same procedure, the relative error of each method has been defined for cloudy and clean sky conditions. The aim is to control whether there is a variation in the model’s relative error performance over various sky conditions. In both cases, RAD (computation using RADIANCE and the Reindl algorithm)performs the best amongst the three methods. Under cloudy and clear sky conditions some 50% of the data show a relative error less than 15 %. More than 80% of the data show a relative error less than 35%. According the results, RAD

DISSCUSION

53

method highly performs in all sky conditions. The correlation of MET and H&K differs for cloudy and clean sky conditions. Under cloudy sky conditions, MET performs better than H&K. However, under clean sky conditions H&K performs better. Figures 40 and 41 show the results. (For further details see Appendix A and Appendix B).

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"


H&K) of vertical irradiance values, North, East, South and West) under cloudy sky conditions

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50


Per

cent

age

of R

esul

ts [

% ]

"MET" "RAD" "H&K"


H&K) of vertical irradiance values, North, East, South and West) under clear sky conditions

DISSCUSION

54

To summarize:

The rather short period of data collection and the resulting small set of data may not warrant a final judgment as to the relative performance of the three methods in view of their reliability in general and their applicability in the Vienna, Austria in particular. However, if we assume that the currently available empirical data represents a good sample of the sky conditions the following provisional conclusions can be derived:

1. Based on the criteria of high correlation and a small range of error, “RAD” model performs the best in the prediction of vertical irradiance values on vertical walls amongst the three methods considered in the research. MET and H&K poorly perform. Their relative error for each orientation is high.

2. The current data suggests the following provisional ranking among the methods:

Table 4 Relative performance of the three methods with regards to the measured data

Method Rank RAD IH&K IIMET III

3. RAD and MET methods appear to perform better under cloudy conditions and H&K method performs better under clear sky condition. However, in both cases (under clear and cloudy sky conditions) RAD shows a low relative error and a high correlation. One can say that RAD performs very well in various sky conditions. To illustrate this point, the performance of the methods for a typical clear and cloudy day is compared: 10th of April 2006 is used as an example to illustrate a typical clear day and 6th of April 2006 is used to illustrate a typical cloudy day. Figures 42-47 illustrate the results for the East, South façade and all orientations.

DISSCUSION

55

East façade

050

100150200250300350400

Irrad

ianc

e [ W

• m

•² ]

Measured valuesComputed values ( method:H&K)Computed values ( method:RAD)Computed values ( method:MET)

Figure 42 Comparison of the results under cloudy sky conditions (East)

0

200

400

600

800

1000

Irrad

ianc

e [ W

• m

•² ]


Figure 43 Comparison of the results under clear sky conditions (East)

DISSCUSION

56

South façade

0

200

400

600

800

1000Irr

adia

nce

[ W •

m •²

]


Figure 44 Comparison of the results under cloudy sky conditions (South)

0

100

200

300

400

500

600

Irrad

ianc

e [ W

• m

•² ]


Figure 45 Comparison of the results under clear sky conditions (South)

DISSCUSION

57

All orientations

0

100

200

300

400

500

600Irr

adia

nce

[ W •

m •²

]


Figure 46 Comparison of the results under cloudy sky conditions (All orientations)

0

200

400

600

800

1000

Irrad

ianc

e [ W

• m

•² ]


Figure 47 Comparison of the results under clear sky conditions (All orientations)

DISSCUSION

58

4. The methods display a tendency toward overestimating the vertical irradiance values. Figures 48-50 illustrate the comparison of the prediction versus measured regression lines (a: RAD, b: H&K, c: MET) under all sky conditions as well as under cloudy and clear sky conditions.

Figure 48: Prediction vs measurement regression lines for the three methods (a: RAD, b: H&K, c: MET)

Figure 49 prediction vs measurement regression lines under cloudy sky conditions for the three methods (a: RAD, b: H&K, c: MET)

DISSCUSION

59

Figure 50 prediction vs measurement regression lines under clear sky conditions for the three methods (a: RAD, b: H&K, c: MET)

CONCLUSION

60

7 CONCLUSION

7.1 Case Study

Based on the high correlation and low relative error RAD methods performs the best among the methods. This method is going to be applied to an ongoing project “People as Power Plants” at the department of Building Physics and Building Ecology.

7.1.1 Overview

The case study investigates the implications of “RAD” (as the method with the best performance) and “H&K” for the computational prediction of the vertical irradiance values for east façade of a multi-storey educational building of Vienna University of Technology.

7.1.2 Approach

H&K and “RAD” models which are described in section 3 are considered. An office building in a multi-storey educational building of Vienna University of Technology was selected for the simulation. The simulation was performed over a period of 31 days (March 2005). A total of 240 time-averaged (hourly) vertical irradiance values were used for the purpose of this study. The facade regarding only the fifth floor of the building has been taken into consideration. The situation of the building and obstructions in terms of the surrounding environment are considered important factors during the simulation procedure. The building is directed to the North with an angle of 16 º (Figure 51). According to the situation, azimuth and other parameters which are needed to computationally derive the vertical irradiance values are defined. Figure 53 illustrates the office rooms on the

CONCLUSION

61

fifth floor (Figure 55) taken into consideration to computationally derive vertical irradiance values using RAD and H&K methods.

The following measurements are taken and data stored on an hourly basis from 7 a.m. to 7 p.m. daily.

i. Global horizontal irradiance

ii. Outdoor temperature (Ta) relative humidity and solar altitude

Table 7 illustrates the other parameters needed to define the vertical irradiance values.

Table 5: The parameters the case-study multi-storey educational building needed to define the vertical irradiance values

Latitude and longitude 48° 12 & 16° 22

See level 202 m

Turbidity factor 2.5

Reitz factor 0.333

Obstructions Near horizon

Azimuth 16 ° from North

Figure 51 illustrates the situation of the building and the surrounding environment Azimuth of the building is defined.

Figure 51: The situation of the multi-storey educational building (Freihaus) and its surrounding environment

CONCLUSION

62

Figure 52: 3d model of the Freihause building

Figure 53: Freihause building plan (5th floor) showing the offices directed to the East orientation.

CONCLUSION

63

7.1.3 Results

The vertical irradiance values are computed using RAD and H & K methods. Figures 54-57 illustrate the results.

0

100

200

300

400

500

600

700

1 2 2 2 2 3 3 4 4 4 4 4 4 5 5 6 6 6 6 6 6 7 7 7 7 7 7

MEASURED "RAD" "H&K"

Figure 54: Measured horizontal irradiance versus “RAD” and “H&K” methods (first week)

0

100

200

300

400

500

600

700

800

8 8 8 8 9 9 9 9 10 10 11 11 11 12 12 12 12 13 13 14 14 14 14


Figure 55: Measured horizontal irradiance versus “RAD” and “H&K” methods (second week)

CONCLUSION

64

0

100

200

300

400

500

600

700

800

900

8 8 8 8 9 9 9 9 10 10 11 11 11 12 12 12 12 13 13 14 14 14 14


Figure 56: Measured horizontal irradiance versus “RAD” and “H&K” methods

0

100

200

300

400

500

600

700

800

15 15 15 16 16 17 17 17 18 18 19 19 19 20 20 21 21 22 22 23 23 23 24 24


Figure 57: Measured horizontal irradiance versus “RAD” and “H&K” methods

CONCLUSION

65

7.2 Contribution

The purpose of this study was to computationally derive vertical irradiance values from measured global horizontal irradiance data and to explore the divergence of predicted irradiance values on building facades based on these methods (referred here as H&K, RAD, MET).

The thesis addresses the need to obtain reliable information on the magnitudes of incident solar radiation on building facades as crucial input for the simulation of the solar energy systems. Vertical irradiance levels were derived using only horizontal irradiance values, which in contrast to concurrent measurements of horizontal global and horizontal diffuse (or direct normal) irradiance data, are available in many locations.

Based on measured global irradiance values, three methods (referred here as H&K, RAD, MET) were applied to compute incident vertical irradiance values. Corresponding photometric measurements have been used to compare the outdoor vertical solar radiation. The computationally derived values were compared with the corresponding measurements and the method’s performance is ranked. Based on these results, the following conclusions were made:

• Degree of achievable accuracy amongst the methods

The methods were compared based on their correlation and relative error. It was concluded that the predicted vertical irradiance values vary considerably. In addition, RAD methods (involving the use of the RADIANCE lighting simulation system and the algorithm suggested by Reindl et al.) performed the best amongst the methods.

• Variation in the methods’ performance over various sky conditions

The evaluation of the methods’ performance under sky conditions showed that RAD performs the best under clear and cloudy sky conditions. However, the performance is higher under cloudy sky conditions. MET has a poor performance under clear sky conditions. On the contrary, H&K has a low performance under cloudy sky conditions. The vertical irradiance values on the West façade for all methods display a high relative error and a law correlation.

CONCLUSION

66

• The methods display the tendency to overestimate the vertical irradiance values.

All the methods display a tendency to overestimate the vertical irradiance values compared with the measurements. The tendencies under clear and cloudy sky conditions for each orientation can be examined at Appendix A, Appendix B.

• The method is applied to an ongoing project

Based on the results it was concluded that the best performing method out of the three considered here provides acceptable results to be applied to an ongoing project application “people as power plants” at the department of building physics and building ecology.

7.3 Potential for future work

This thesis has provided certain results in the area of solar radiation concerning the magnitude of incident solar radiation on building facades as crucial input for the simulation of solar energy systems. Further development efforts are required and directions for the future research can be identified.

As mentioned earlier, the results presented in this research will have to be further scrutinized as more measured data is collected. Thus, future research can involve the collection of additional data. The measured data used for this research has been collected in a period of 16 days in November 2005 and April 2006. Far more data in seasonal or annual basis and in different climate conditions is needed to explore the potentials of the models` regarding vertical irradiance values. The initial results suggest that under clear sky conditions for West facade all the methods perform poorly. This needs to be further tested under clear sky conditions with higher horizontal irradiance levels.

In addition, it has to be explored if the algorithms to computationally derive vertical irradiance values from measured irradiance levels on building facades can be improved in the future (e.g. via the study of the diffuse and direct radiation components under various sky conditions).

67

REFERENCES

Cornelis, P. J. , De Wilde, J. 2004. “Computational Support for the Selection of Energy Saving Building Components”. Delft University Press, Netherlands. Danny, H.W. Li, Joseph C. L. 1999. “Measurements of solar radiation and illuminance on vertical surfaces and daylighting implications”. Building Energy Research Group, Department of Building and Construction, Renewable Energy 20 (2000) 389±404, City University of Hong Kong.Dijk, H.1987. “Thermal and solar properties of windows”. Institute of Applied Physics, Delft.Duffie, J.A., and Beckman, W. A. 1980. “Solar engineering of thermal processes”. Wiley-Interscience Publication, pp. 1, 72, New York.Erbs, D.G.1980. “Methods for estimating the diffuse fraction of hourly, daily and monthly-average global solar radiation”. Mechanical Engineering, University of Wisconsin-Madison.Hübe, H. 2000. “Office worker preferences of exterior shading devices: A pilot study”. Department of Construction and Architecture, Lund University, Lund, Sweden.Lee, E.S., Rubinstein, F.M., and Selkowitz, S.E. 1996. “Developing a Dynamic Envelope/Lighting Control System with Field Measurements”. National Laboratory University of California.Le, E S., Di Bartolomeo, D.L., and Selkowitz, S.E. 1999. “Thermal and Daylighting Performance of an Automated Venetian Blind and Lighting System in a Full Scale Private Office”. Building Technologies Program Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA USA 94720.Lee, E.S., Di Bartolomeo, D.L., Vine, E.L., and Selkowitz, S.E. 1998. “Integrated Performance of an Automated Venetian Blind/Electric Lighting System in a Full-ScalePrivate Office”. University of California Berkeley, California.Lee, E.S., Stephen, E., and Selkowitz, G. 1998. “Integrated Envelope and Lighting Systems for Commercial Buildings: A Retrospective”. University of California, Berkeley, CA 94720.Mahdavi, A. 1995. “Fundamentals of Building Physics”. Carnegie Mellon University, Department of Architecture.Meteonorm 2005. Global meteorological database. Version 5.1. URL: www.meteonorm.com.Orgill, J. F., and Hollands, K.G. 1997. “Correlation equation for hourly diffuse radiation on a horizontal surface”. Solar Energy 19, 357.Perez, R., Ineichen, P., Stewart,R., and Seals, R.1987. “Modeling a new simplified version of the Perez diffuse Irradiance model for titled surfaces”. Solar energy Vol 39, 221-231.

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Perez, R., Ineichen, P., and Seals, R. 1990. “Modeling the daylight availability and irradiance components from direct and global irradiance”. Solar energy, 44 (5), 271-289.Perez, R., Seals, R., and Michalsky, J. 1993. “All-weather model for sky luminance distribution-preliminary configuration and validation”. Solar Energy Vol. 50, No. 3, pp. 235-245.Reindl, D.T., Beckman, W.A., and Duffie, J.A. 1990. “Diffuse fraction correlations”. Solar Energy Vol. 45, No. 1, pp. 1-7.Skartweit, A., and Olseth, J. A. 1987. “A model for the diffuse fraction of hourly global radiation”. Solar Energy 38, 271-274.Solar (2005). Solar altitude and azimuth URL: http://www.volker-quaschning.de/datserv/sunpos/index_e.html.Spasojevic, B., and Mahdavi, A. 2005. "Sky luminance mapping for the computational daylight modeling". Proceedings of the 9th International IBPSA Conference. Montreal, Canada. I. Beausoleil-Morrison, M. Bernier (Hrg.); International Conference: IBPSA, 2005, S. 1163 – 1169.Vartiainen, E. 2000. “A new approach to estimating the diffuse irradiance on inclined surfaces”. Renewable Energy. Vol. 20, pp. 45-64.Ward, L. G.., and Shakespeare, R. 2003. “Rendering with Radiance: The Art and Science of Lighting Visualization”. Revised Edition Space and Davis, CA, USA.

69

Appendix A

Comparison of the vertical irradiance values (methods: H&K, RAD and MET) under clear sky conditions

Comparison based on correlation

Computationally derived vertical irradiances values of H&K, RAD and MET methods are compared with measured vertical irradiance values based on their correlation and relative error under cloudy conditions.

Figures 58 shows the comparison of measured and calculated (H&K method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

y = 0.7747x - 3.4987R2 = 0.59940

20406080

100120140160180

0 50 100 150

Computed values using "H&K" (North) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.891x - 16.102R2 = 0.8911

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Computed values using "H&K" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.9202x - 53.776R2 = 0.87850

100

200

300400

500

600

700

800

0 200 400 600 800

Computed values using "H&K" (South) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m •

² ]

y = 0.8275x - 21.799R2 = 0.9004

0

100

200

300400

500

600

700

800

0 200 400 600 800

Computed values using "H&K" (West) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

70

Figure 58 Comparison of measured and calculated (method: H&K) vertical irradiance values under cloudy sky conditions (North, East, South, West façade and All orientations)

Figures 59 shows the comparison of measured and calculated (RAD method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

Figure 59 Comparison of measured and calculated (method: RAD) vertical irradiance values under cloudy sky conditions (North, East, South, West façade and All orientations)

y = 0.8406x - 19.277R2 = 0.8880

100200300400500600700800

0 200 400 600 800

Computed values using "H&K" (All orientations) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•²

]

y = 1.3641x - 8.0287R2 = 0.8270

20406080

100120140160180

0 20 40 60 80 100 120

Computed values using "RAD" (North) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m•²

]

y = 0.8237x + 10.545R2 = 0.9475

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Computed values using "RAD" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.9287x - 16.018R2 = 0.94040

100

200

300

400

500

600

700

800

0 200 400 600 800

Computed values using "RAD" (South) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.8009x + 17.173R2 = 0.822

0

100

200

300

400

500

600

700

0 200 400 600 800

Compued values using "RAD" (West) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.8572x + 8.8192R2 = 0.90780

100200300400500600700800

0 200 400 600 800

Computed values using "RAD" (All orientations) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•²

]

71

Figures 60 shows the comparison of measured and calculated (MET method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

Figure 60 Comparison of measured and calculated (method: MET) vertical irradiance values under cloudy sky conditions (North, East, South, West façade and All orientations)

y = 0.4159x + 19.749R2 = 0.5497

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Computed values using "MET" (North) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.5351x + 6.5773R2 = 0.92710

100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "MET" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]y = 0.7864x - 5.9174

R2 = 0.94590100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "MET" [ W• m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.8656x - 8.3778R2 = 0.89920

100

200

300

400

500

600

700

800

0 200 400 600 800

Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.7644x - 5.626R2 = 0.86640

100200300400500600700800

0 200 400 600 800 1000

Computed values using "MET" (All orientations) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•²

]

72

§ Comparison based on correlation

The figure 61 shows comparison of relative error of North, East; South and West façade vertical irradiance values for H&K, RAD and MET methods under cloudy sky conditions.

Figure 61: Comparison of cumulative error and percentage of results (method: H&K, RAD and MET)

of vertical irradiance values (North, East; South and West façade)

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (MET)

Per

cent

age

of R

esul

ts [

% ]


0

10

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30

40

50

60

70

80

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100

5 10 15 20 25 30 35 40 45 50

Cumulat ive Error [ ± % ] (H&K)

Perc

enta

ge o

f Res

ults

[ %

]


0

1020

30

40

5060

70

80

90100

5 10 15 20 25 30 35 40 45 50

Cumulat ive Error [ ± % ] (RAD)

Perc

enta

ge o

f Res

ults

[ %

]


73

H&K, RAD and MET models are compared for each orientation separately. The aim is to explore which model performs the best based on each orientation. Figure 62 shows the results.



The figure 63 shows the cumulative error comparison versus the percentage of results of MET, RAD, and H&K methods for all orientations. (North, East, South and West)


of vertical irradiance values (All orientations)

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (All orientations)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0

10

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40

5060

70

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100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (North)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (East)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (South)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RED" "H&K"

010

2030

4050

6070

8090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (West)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

74

Appendix B

Comparison of the vertical irradiance values (methods: H&K, RAD and MET) under clear sky conditions

§ Comparison based on correlation

Computationally derived vertical irradiances values of H&K, RAD and MET methods are compared with measured vertical irradiance values based on their correlation and relative error under cloudy conditions.

Figures 64 shows the comparison of measured and calculated (H&K method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

y = 1.1459x - 128.38R2 = 0.90640

100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "H&K" (South) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.4934x + 51.288R2 = 0.47170

50100150200250300350400450500

0 100 200 300 400 500

Computed values using "H&K" (West) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.9923x - 21.23R2 = 0.63470

20406080

100120140160180200

0 50 100 150

Computed values using "H&K" (North) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.9577x + 0.6713R2 = 0.73120

50100150200250300350400450500

0 100 200 300 400 500

Computed values using "H&K" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

75

Figure 64 Comparison of measured and calculated (method: H&K) vertical irradiance values under clear sky conditions (North, East, South, West façade and All orientations)

Figures 65 shows the comparison of measured and calculated (RAD method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

Figure 65 Comparison of measured and calculated (method: RAD) vertical irradiance values under clear sky conditions (North, East, South, West façade and All orientations)

y = 0.9117x - 19.501R2 = 0.85750

200

400

600

800

1000

0 200 400 600 800 1000

Computed values using "H&K" (All orientations) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m

•²

]

y = 1.5698x - 22.055R2 = 0.84010

20406080

100120140160180200

0 20 40 60 80 100 120 140

Computed values using "RAD" (North) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m•²

]

y = 0.8186x + 25.208R2 = 0.79610

50100150200250300350400450500

0 100 200 300 400 500 600

Computed values using "RAD" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 1.1292x - 75.705R2 = 0.93420

100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "RAD" (South) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.5474x + 70.814R2 = 0.4224

0

50

100

150

200

250

300

350

0 100 200 300 400 500

Compued values using "RAD" (West) [ W • m •² ]

Mea

sure

d va

lues

[ W

•m •

² ]

y = 0.9384x + 7.9294R2 = 0.8934

0100200300400500600700800900

0 200 400 600 800 1000

Computed values using "RAD" (All orientations) [ W • m •² ]

Measu

red v

alu

es

[ W

•m

•²

]

76

Figures 66 shows the comparison of measured and calculated (MET method) vertical irradiance values for North, East, South West and all orientations under cloudy sky conditions.

Figure 66 Comparison of measured and calculated (method: MET) vertical irradiance values under clear sky conditions (North, East, South, West façade and All orientations)

y = 0.4103x + 22.53R2 = 0.586

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Computed values using "MET" (North) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.556x + 13.276R2 = 0.6988

0100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "MET" (East) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.8157x + 11.656R2 = 0.8002

0100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "MET" (South) [ W• m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.4599x + 76.083R2 = 0.2288

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400

Computed values using "MET" (West) [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

y = 0.7834x - 4.4591R2 = 0.78850

100200300400500600700800900

1000

0 200 400 600 800 1000

Computed values using "MET" [ W • m •² ]

Mea

sure

d va

lues

[

W •m

•²

]

77

• Comparison based on relative error

The figure 67 shows comparison of relative error of North, East; South and Westfaçade vertical irradiance values for H&K, RAD and MET methods under cloudy sky conditions.


of vertical irradiance values (North, East; South and West façade)

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (MET)

Perc

enta

ge o

f Res

ults

[ %

]


0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] ("H&K" Method )

Perc

enta

ge o

f Res

ults

[ %

]


0

10

2030

4050

6070

80

90100

5 10 15 20 25 30 35 40 45 50

Cumulat ive Error [ ± % ] ("RAD" Method)Pe

rcen

tage

of

Res

ults

[ %

]


78

Figure 68 illustrates the comparison of the relative error of H&K, RAD and MET for each orientation separately.



The figure 69 shows the cumulative error comparison versus the percentage of results of MET, RAD, and H&K methods for all orientations. (North, East, South and West)


of vertical irradiance values (All orientations)

0

10

20

30

40

50

60

70

80

90

100

5 10 15 20 25 30 35 40 45 50

Cumulat ive Error [ ± % ] (All Orientations)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0

10

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50

607080

90

100

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Cumulative Error [ ± % ] (North)

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enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0102030405060708090

100

5 10 15 20 25 30 35 40 45 50

Cumulative Error [ ± % ] (East)

Perc

enta

ge o

f Res

ults

[ %

]

"MET" "RAD" "H&K"

0102030405060708090

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5 10 15 20 25 30 35 40 45 50


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cent

age

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ts [

% ]

"MET" "RED" "H&K"

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cent

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ts [

% ]

"MET" "RAD" "H&K"

79

Appendix C

The Procedure for the estimation of radiation incident on arbitrarily inclined surfaces (H&K method)

The program calculates solar irradiance for a defined point in two components of direct and diffuse irradiance. Obstacles, geographic coordinates, see level and angles of the surface are the inputs of the program. The azimuth of each surface is defined. The obstacles’ angles for each inclined surface in three levels close, middle and far horizon can be calculated. The output of diffuse and direct components has a predefined format. The next step is the interpolation (15 minute basis) procedure using Sunselect software program. Figure 70-74 illustrate the inputs and procedure that the simulation program requires to computationally derive the vertical irradiance values.

Figure 70: The inputs of the H&K methods

Geographic coordinates

See level

Turbidity and Reitz factor

80

Figure 71: Defining the azimuth of each surface/point.

Figure 72: Obstacles’ angels for each point in three levels, close horizon, middle and far horizon.

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Sonnenstand Horizont Einfalls Strahlungsflüsse [W/m²]Uhr Azimut Höhe höhe winkel Direkt Himmel Reflex Diffus Global1 h - - - - - - 1.0° - - - - - - - - - - - - - - - - - -2 h - - - - - - 2.0° - - - - - - - - - - - - - - - - - -3 h - - - - - - 2.0° - - - - - - - - - - - - - - - - - -4 h - - - - - - 3.1° - - - - - - - - - - - - - - - - - -5 h - - - - - - 3.4° - - - - - - - - - - - - - - - - - -6 h - - - - - - 2.4° - - - - - - - - - - - - - - - - - -7 h 105.2° 2.7° 3.5° 2.8° - - - 9.0 1.8 10.8 10.88 h 116.9° 11.9° 5.4° 16.1° 567.7 27.5 17.7 45.1 612.89 h 129.7° 20.2° 4.1° 30.7° 663.1 35.7 33.8 69.5 732.610 h 144.1° 27.0° 4.0° 45.5° 607.6 39.7 47.3 87.1 694.711 h 160.3° 31.7° 4.0° 60.2° 454.5 41.8 56.4 98.2 552.712 h 177.8° 33.6° 4.2° 74.9° 242.7 42.4 60.0 102.5 345.213 h 195.4° 32.4° 1.4° 89.5° 7.7 42.0 57.8 99.9 107.614 h 212.0° 28.4° 0.0° 104.0° - - - 40.4 50.1 90.5 90.515 h 226.9° 22.1° 0.0° 118.4° - - - 37.0 37.5 74.5 74.516 h 240.0° 14.1° 0.0° 132.4° - - - 30.1 21.8 51.9 51.917 h 251.9° 5.1° 0.0° 145.6° - - - 15.2 6.2 21.4 21.418 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -19 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -20 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -21 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -22 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -23 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -24 h - - - - - - 0.0° - - - - - - - - - - - - - - - - - -

Figure 73: A sample of the output file format (predefined in one hour basis)

Figure 74: The interpolation procedure using Sunselect software program

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Appendix D

The Procedure for the estimation of radiation incident on arbitrarily inclined surfaces (MET method)

This application allows for the estimation of radiation incident on arbitrarily oriented surfaces based on available measured global horizontal irradiance and outdoor air temperature values. Figure 75-77 illustrate the inputs and procedure that the simulation program requires to computationally derive the vertical irradiance values.

Figure 75: Defining the inputs of the ‘MET’ to computationally derive vertical irradiance values

Geographic coordinates

Azimuth and Inclination

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Figure 76: The parameters required (Global horizontal irradiance and outdoor temperature) to computationally derive vertical irradiance values

Figure 77: The output format of MET

Output variable

computational derivation of incident irradiance on ... · 1. that i am the sole author of the...

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